When GSX Control is on, you can't control the inibuilds GPU anymore. But this is the one which actually provides power to the aircraft.

I can request the GSX GPU, but then I only get the animation, but no power to the aircraft.

So I have to connect the inibuilds GPU, turn GSX control on, do the fueling and boarding, turn it off again, and then I can disconnect the GPU.

I once started push back with the ini GPU still attached. Eventually it was gone from the aircraft. Still no way to connect it again after arriving at the gate without turning GSX control off.

This is really something to get solved. Or am I'm missing something in the procedure with GSX and the A350?

you need to go to the grnd/gsx/other than select dismiss gpu

If you mean dismiss the GSX GPU, that won't do anything to the inibuilds GPU (shown in orange and with the symbol). When GSX control is on ,the GPU is greyed out.